Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Citation:

Serdica Mathematical Journal, Vol. 25, No 3, (1999), 207p-240p

Abstract:

The general ordinary quasi-differential expression M of n-th order
with complex coefficients and its formal adjoint M + are considered over
a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator
may have a finite number of singular points. By considering M over various
subintervals on which singularities occur only at the ends, restrictions of the
maximal operator generated by M in L2|w (a, b) which are regularly solvable
with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to
direct sums of regularly solvable operators defined on the separate subintervals,
there are other regularly solvable restrications of the maximal operator
which involve linking the various intervals together in interface like style.